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Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operators

Author

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  • Anjum, Rizwan
  • Din, Muhammad
  • Zhou, Mi

Abstract

The aim of this paper is to introduce and develop two novel classifications of enriched (q,θ)-contractions on Banach spaces. The paper includes illustrative examples to demonstrate these concepts and establishes the convergence of Krasnoselskii’s iteration method when applied to approximate the fixed point of such enriched (q,θ)-contractions. Additionally, the paper explores the application of these concepts in constructing the fractals of the corresponding Hutchinson–Barnsley operators. The above construction is illustrated by some examples. These discoveries provide new fixed-point solutions for iterated function systems under various contractive conditions. Finally, as an application of our main result, the existence of the solution to the problem of fourth order differential equation is presented. Furthermore, the findings not only validate but also enhance and expand upon multiple established conclusions in the existing literature.

Suggested Citation

  • Anjum, Rizwan & Din, Muhammad & Zhou, Mi, 2024. "Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001401
    DOI: 10.1016/j.chaos.2024.114589
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    References listed on IDEAS

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    1. Fahim Ud Din & Muhammad Din & Umar Ishtiaq & Salvatore Sessa, 2023. "Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation," Mathematics, MDPI, vol. 11(1), pages 1-18, January.
    2. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

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